SOLUTION: a certain two digit is 13 more than 9 times the tens digit. the original number is 4 less than twice the number formed by interchanging the digits. Find the original number
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Question 545799: a certain two digit is 13 more than 9 times the tens digit. the original number is 4 less than twice the number formed by interchanging the digits. Find the original number Answer by mananth(16946) (Show Source):
9 x + 13 = 10 x+ y
9 x -10 x - y = -13
-1 x + -y= -13 -----------------------------(1)
10 x+ y = 2 ( 10 y+ x)- 4
10 x+ y = 20 y + 2 x - 4
10 x - 2 x + -20 y = -4
8 x + -19 y = -4 --------------(2)
Solve equation (1) & (2) for x & y
-1 x -1 y = -13 .............1
8 x -19 y = -4 .............2
-19 y
multiply (1)by -19
Multiply (2) by 1
19 x 19 y = 247
8 x + -19 y = -4
Add the two equations
27 x = 243.000
/ 27
x = 9
plug value of x in (1)
-1 x + -1 y = -13
-9 + -1 y = -13
-1 y = -13 + 9
-1 y = -4
y = 4
